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An Extension of the Class of Regularly Varying Functions

Author

Listed:
  • Cadena, Meitner

    (UPMC (Université Pierre-et-Marie-Curie) à Paris 6 & CREAR (Center of Research in Econo-finance and Actuarial sciences on Risk) at ESSEC)

  • Kratz, Marie

    (ESSEC Business School)

Abstract

We define a new class of positive and Lebesgue measurable functions in terms of their asymptotic behavior, which includes the class of regularly varying functions. We also characterize it by transformations, corresponding to generalized moments when these functions are random variables. We study the properties of this new class and discuss their applications to Extreme Value Theory.

Suggested Citation

  • Cadena, Meitner & Kratz, Marie, 2014. "An Extension of the Class of Regularly Varying Functions," ESSEC Working Papers WP1417, ESSEC Research Center, ESSEC Business School.
    • Handle: RePEc:ebg:essewp:dr-14017
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    File URL: https://hal-essec.archives-ouvertes.fr/hal-01097780/document
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    References listed on IDEAS

    as
    1. Daley, D.J. & Goldie, Charles M., 2006. "The moment index of minima (II)," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 831-837, April.
    2. Hadar, Josef & Russell, William R., 1971. "Stochastic dominance and diversification," Journal of Economic Theory, Elsevier, vol. 3(3), pages 288-305, September.
    3. de Haan, L. & Resnick, S. I., 1981. "On the observation closest to the origin," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 301-308, August.
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    Cited by:

    1. Wei Jiang & Steven Kou, 2021. "Simulating risk measures via asymptotic expansions for relative errors," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 907-942, July.

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    More about this item

    Keywords

    asymptotic behavior - domains of attraction; extreme value theory; Karamata’s representation theorem; Karamata’s theorem; Karamata’s tauberian theorem; measurable functions; von Mises’ conditions; Peter and Paul distribution; regularly varying function;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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